(r-s)(x)

Suppose r(x) = 3+4/x^2+1, s(x)= x^+6/6x-1.Write the expression (r-s)(x) as a simplified ratio with the numerator and denominator each written as a sum of terms of the form cx^m and c>0 for the term with the highest power in the numerator. I ended up with (-x^4+11x^2+21x-10)/-6x^3+x^2-6x+1. Where did I go wrong here?

Re: (r-s)(x)

The only way I got the answer right was when I subtracted s with r instead of r - s. It looked like this with the polynomial subtraction (x^4 + 7x^2 + 6)-(18x^2+21x-4). And it gives me x^4-11x^2+21x+10 for the numerator.

Re: (r-s)(x)

Re: (r-s)(x)

Changing the sign of both the numerator and the denominator (i.e., multiplying both by -1) does not change the fraction. The problem asks for a fraction with a positive leading coefficient in the numerator.

Re: (r-s)(x)

Originally Posted by Eraser147

Suppose r(x) = 3+4/x^2+1,

Do you mean 3+ 4/(x^2+ 1)?

s(x)= x^+6/6x-1.

What should be after the "^"? Do you mean x^?+ 6/(6x- )? Or (x^?+ 6)(6x- 1)?

Write the expression (r-s)(x) as a simplified ratio with the numerator and denominator each written as a sum of terms of the form cx^m and c>0 for the term with the highest power in the numerator. I ended up with (-x^4+11x^2+21x-10)/-6x^3+x^2-6x+1. Where did I go wrong here?

Re: (r-s)(x)

Oh, I already figured it out. Emakarov showed it. My mistake was not flipping the signs by multiplying -1 from numerator and denominator since the problem asked for the leading term to be a positive number and the constant to be more than zero. Read the post above to find the image of the actual equation if you are interested.